barry100r. 180KB Jun 04 2011 12:06:47 AM
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In this paper, we find an explicit formula for the generating function for the number of partitions of [ n ] with exactly k blocks according to the number of peaks (valleys) in terms
(1) There seems to be a general principle that if an existence result about polynomials or n -tuples of polynomials over an infinite field can be proved by dimension counting, then
in this case, one can also appeal to the Hermite-Biehler theorem: if S and T are nonconstant polynomials with real coefficients, then the polynomials S and T have interlacing zeros
A publication of the International Linear
Both infinite and sequences of finite Toeplitz matrices are considered, and also studied is the finite section method, which consists in approximating infinite systems by large
We remark that our approach of using orthogonal polynomials to control the density pointwise was motivated by the work of Pastur and Shcherbina [26], where they proved sine-kernel
In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest
Key words: orthogonal polynomials; Askey–Wilson polynomials; q-difference equation; three term recurrence; raising operators; lowering operators; root systems; double affine
